The Istanbul giants are close to agreeing personal terms with Kolarov and want to keep his salary under £2.5 million per-season.
Besiktas initially wanted to loan Kolarov due to their commitment to the Financial Fair Play investigation they are currently under but have struck a mutually agreeable deal for a permanent transfer.
The deal rests on whether Kolarov will accept Besiktas’ salary offer as they will be unable to match a higher fee.
Despite wining the league title last season Besiktas conceded more goals than any other side in the top three – while scoring the highest number of goals in the league.
The Black Eagles are keen on bolstering their defensive line having booked a place in the Champions League group stages next season.